Finite Group Databasebeta

← #30603298

Subgroups — #30603298

Order 15616.

850 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D61⋊#108C211yesmaximal, characteristic, complemented
2C2×#16840748C212yesmaximal
3#21461511C211yesmaximal, characteristic, complemented
4C2×#16840631C212yesmaximal, complemented
5C2×#16839727C211yesmaximal, characteristic
6C2×D61⋊M16C2212yes—
7C2×D61⋊M16C2212yes—
8C2×#14519848—21no—
9D61⋊#108—24no—
10C2×#14519847—21no—
11#16840748—24no—
12#16840748—24no—
13C2×#14519838—22no—
14C2×#14519837—22no—
15#16840638—21no—
16#16840638—21no—
17#16840631—24no—
18C22×#11758222C2211yescharacteristic
19C22×#11758189C2211yescharacteristic
20C22×C8×D61C2211yescharacteristic
21#16839727—21no—
22#16839727—21no—
23#16839727—21no—
24#16839727—21no—
25C2×C22⋊#92418C411yescharacteristic
26C2×#14519689C411yescharacteristic
27C2×#14519689C411yescharacteristic
28C2×C22⋊C8×C61C411yescharacteristic
29C2×#11758213—22no—
30C2×#11758213—22no—
31D61⋊M16—22no—
32D61⋊M16—22no—
33D61⋊M16—22no—
34D61⋊M16—22no—
35D61⋊M16—22no—
36D61⋊M16—22no—
37D61⋊M16D414yes—
38D61⋊M16D414yes—
39C2×#11758217—22no—
40C2×#11758217—22no—
41C2×D61⋊C8—22no—
42C2×D61⋊C8—22no—
43#14519848—24no—
44#14519847—24no—
45#14519838—28no—
46#14519837—28no—
47C2×#11758222—22no—
48C2×#11758222—22no—
49C2×#11758222—21no—
50C2×#11758222—21no—
51C2×#11758222—21no—
52C2×#11758222—21no—
53C2×#11758222—22no—
54C2×#11758222—22no—
55C22×Dic122D411yescharacteristic
56C22×D244Q811yescharacteristic
57C22×C22⋊D61D411yescharacteristic
58C22×C22⋊D61Q811yescharacteristic
59C22×C4×D61C2×C411yescharacteristic
60C22×C4×D61C2311yescharacteristic
61C2×#11758189—21no—
62C2×#11758189—21no—
63C2×#11758189—22no—
64C2×#11758189—22no—
65C22×#92418C2×C411yescharacteristic
66C22×#92418C2×C411yescharacteristic
67C2×C8×D61—22no—
68C2×C8×D61—22no—
69C2×C8×D61D411yescharacteristic
70C2×C8×D61D411yescharacteristic
71C2×C8×D61D411yescharacteristic
72C2×C8×D61D411yescharacteristic
73C22⋊#92418—21no—
74C22⋊#92418—21no—
75#14519689—21no—
76#14519689—21no—
77#14519689—21no—
78#14519689—21no—
79C23×C4×C61C2×C411yescharacteristic
80C22×C8×C61C2×C411yescharacteristic
81C22×C8×C61C2×C411yescharacteristic
82C22⋊C8×C61—21no—
83C22⋊C8×C61—21no—
84C24×C61C4⋊C411yescharacteristic
85C23×D61C4⋊C411yescharacteristic
86C23×D61C2×Q811yescharacteristic
87C22×C4×C61—21no—
88C22×C4×C61—21no—
89C22×C4×C61—22no—
90C22×C4×C61—22no—
91C22×C4×C61C4⋊C411yescharacteristic
92C22×C4×C61C22×C411yescharacteristic
93C2×C22⋊D61—21no—
94C2×C22⋊D61—21no—
95C2×C22⋊D61—22no—
96C2×C22⋊D61—22no—
97C2×C22⋊D61—22no—
98C2×C22⋊D61—21no—
99C2×C22⋊D61—21no—
100C2×C22⋊D61—22no—
101C22×Dic61C4⋊C411yescharacteristic
102C22×Dic61C2×D411yescharacteristic
103#11758222—41no—
104#11758222—42no—
105#11758222—42no—
106#11758222—42no—
107#11758222—42no—
108#11758222—41no—
109#11758222—42no—
110#11758222—41no—
111#11758222—42no—
112#11758222—41no—
113C2×D244—22no—
114C2×D244—21no—
115C2×D244—21no—
116C2×D244—22no—
117C2×C4×D61—21no—
118C2×C4×D61—21no—
119C2×C4×D61—22no—
120C2×C4×D61—22no—
121C2×C4×D61C2×D412yes—
122C2×C4×D61C2×D411yescharacteristic
123C2×C4×D61C2×D411yescharacteristic
124C2×C4×D61C2×D412yes—
125C2×C4×D61#4111yescharacteristic
126C2×C4×D61#4112yes—
127C2×C4×D61#4112yes—
128C2×C4×D61#4111yescharacteristic
129C2×Dic122—22no—
130C2×Dic122—21no—
131C2×Dic122—21no—
132C2×Dic122—22no—
133#11758217—24no—
134#11758217—24no—
135#11758217—42no—
136#11758217—42no—
137C2×#92420—42no—
138C2×#92420—42no—
139#11758213—24no—
140#11758213—24no—
141#11758213—42no—
142#11758213—42no—
143D61⋊C8—24no—
144D61⋊C8—24no—
145D61⋊C8—42no—
146D61⋊C8—42no—
147C2×C8×C61—22no—
148C2×C8×C61—21no—
149C2×C8×C61—22no—
150C2×C8×C61C22⋊C411yescharacteristic
151C2×C8×C61C22⋊C411yescharacteristic
152C2×#92418—22no—
153C2×#92418—21no—
154C2×#92418—22no—
155C2×#92418C22⋊C411yescharacteristic
156C2×#92418C22⋊C411yescharacteristic
157#11758189—42no—
158#11758189—41no—
159#11758189—41no—
160C8×D61—21no—
161C8×D61—21no—
162C8×D61—22no—
163C8×D61—22no—
164C8×D61—21no—
165C8×D61—21no—
166C23×C61—21no—
167C23×C61—22no—
168C23×C61—41no—
169C23×C61—41no—
170C23×C61C2×C4⋊C411yescharacteristic
171C22×D61—21no—
172C22×D61—22no—
173C22×D61—41no—
174C22×D61—41no—
175C22×D61—41no—
176C22×D61—41no—
177C22×D61C22⋊Q811yescharacteristic
178C22×D61C22⋊Q811yescharacteristic
179C22×D61C22⋊Q812yes—
180C22×D61C22⋊Q812yes—
181C2×C4×C61—21no—
182C2×C4×C61—22no—
183C2×C4×C61—41no—
184C2×C4×C61—42no—
185C2×C4×C61—41no—
186C2×C4×C61C2×C22⋊C411yescharacteristic
187C2×C4×C61#11711yescharacteristic
188C2×C4×C61C4×D412yes—
189C2×C4×C61C4×D412yes—
190C22⋊D61—41no—
191C22⋊D61—42no—
192C22⋊D61—41no—
193C22⋊D61—41no—
194C22⋊D61—42no—
195C22⋊D61—41no—
196C2×Dic61—21no—
197C2×Dic61—22no—
198C2×Dic61#12012yes—
199C2×Dic61#12111yescharacteristic
200C2×Dic61#12111yescharacteristic
201C2×Dic61#12312yes—
202D244—41no—
203D244—42no—
204D244—41no—
205C4×D61—41no—
206C4×D61—42no—
207C4×D61—41no—
208C4×D61#12011yescharacteristic
209C4×D61#12112yes—
210C4×D61#12112yes—
211C4×D61#12112yes—
212C4×D61#12312yes—
213C4×D61#12311yescharacteristic
214C4×D61#12412yes—
215C4×D61#12411yescharacteristic
216C4×D61#12612yes—
217C4×D61#12711yescharacteristic
218Dic122—41no—
219Dic122—42no—
220Dic122—41no—
221#92420—44no—
222#92420—44no—
223C8×C61—21no—
224C8×C61—21no—
225C8×C61—41no—
226#92418—21no—
227#92418—21no—
228#92418—41no—
229#11099—611nomaximal, Sylow
230C22×C61—21no—
231C22×C61—21no—
232C22×C61—41no—
233C22×C61—41no—
234C22×C61—41no—
235C22×C61—82no—
236C22×C61#38011yescharacteristic
237C22×C61#38512yes—
238C2×D61—21no—
239C2×D61—21no—
240C2×D61—21no—
241C2×D61—21no—
242C2×D61—42no—
243C2×D61—42no—
244C2×D61—41no—
245C2×D61—41no—
246C2×D61—41no—
247C2×D61—82no—
248C2×D61#39311yescharacteristic
249C2×D61#39612yes—
250C2×D61#39911yescharacteristic
251C4×C61—41no—
252C4×C61#38611yescharacteristic
253C4×C61#38812yes—
254C4×C61#39011yescharacteristic
255Dic61—41no—
256Dic61#39211yescharacteristic
257Dic61#39412yes—
258Dic61#39711yescharacteristic
259C22×#108—611no—
260C2×#413—612no—
261C2×#408—611no—
262C2×#341—611no—
263C2×#338—612no—
264C2×C61—22no—
265C2×C61—81no—
266C2×C61#143911yescharacteristic
267C2×C61#181311yescharacteristic
268C2×C61#181311yescharacteristic
269D61—21no—
270D61—22no—
271D61—21no—
272D61—81no—
273C22×#41—611no—
274C22×M16—611no—
275C22×M16—612no—
276C22×M16—612no—
277C23×C8—611no—
278C2×#108—1221no—
279C2×#108—1221no—
280C2×#108—1224no—
281#413—1224no—
282#413—1224no—
283C2×#101—1222no—
284C2×#100—1222no—
285#408—1221no—
286#408—1221no—
287#408—1221no—
288#408—1221no—
289C2×C22⋊C8—611no—
290C2×C22⋊C8—611no—
291C2×C22⋊C8—611no—
292C2×C22⋊C8#692311yescharacteristic
293#341—1221no—
294#341—1221no—
295#338—1224no—
296C61#1109911yescharacteristic, complemented, Sylow
297C2×#41—1221no—
298C2×#41—1221no—
299C2×#41—1222no—
300C2×#41—1222no—
301C2×#41—1221no—
302C2×#41—1221no—
303C2×#41—1222no—
304C2×#41—1222no—
305C22×Q8—611no—
306C22×D4—611no—
307C22×D4—611no—
308C22×D4—611no—
309C23×C4—611no—
310C23×C4—611no—
311C23×C4C2×#692311yescharacteristic
312C2×M16—614no—
313C2×M16—614no—
314C2×M16—1222no—
315C2×M16—1221no—
316C2×M16—1221no—
317C2×M16—1222no—
318C2×M16—1222no—
319C2×M16—1222no—
320C2×M16—1222no—
321C2×M16—1222no—
322C2×M16—1222no—
323C2×M16—1222no—
324C2×M16—1222no—
325C2×M16—1222no—
326C2×M16—1222no—
327C2×M16—1222no—
328C22×C8—611no—
329C22×C8—611no—
330C22×C8—611no—
331C22×C8—611no—
332C22×C8—611no—
333C22×C8—611no—
334C22×C8—1222no—
335C22×C8—1222no—
336C22×C8—1222no—
337C22×C8—1222no—
338C22×C8C2×#692311yescharacteristic
339C22×C8C2×#692311yescharacteristic
340#108—1224no—
341#108—1224no—
342#101—1228no—
343#100—1228no—
344C22⋊C8—21no—
345C22⋊C8—21no—
346C22⋊C8—1221no—
347C22⋊C8—1221no—
348C22⋊C8—1221no—
349C22⋊C8—1221no—
350C22⋊C8—1221no—
351C22⋊C8—1221no—
352C24—611no—
353C24—611no—
354C24C4⋊#692311yescharacteristic
355#41—2441no—
356#41—2442no—
357#41—2441no—
358#41—2442no—
359#41—2442no—
360#41—2442no—
361#41—2442no—
362#41—2442no—
363#41—2441no—
364#41—2441no—
365C2×Q8—1222no—
366C2×Q8—1221no—
367C2×Q8—1221no—
368C2×Q8—1222no—
369C2×D4—1221no—
370C2×D4—1221no—
371C2×D4—1222no—
372C2×D4—1222no—
373C2×D4—1222no—
374C2×D4—1221no—
375C2×D4—1221no—
376C2×D4—1222no—
377C2×D4—1221no—
378C2×D4—1221no—
379C2×D4—1222no—
380C2×D4—1222no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—611no—
386C22×C4—611no—
387C22×C4—611no—
388C22×C4—611no—
389C22×C4—611no—
390C22×C4—612no—
391C22×C4—612no—
392C22×C4—612no—
393C22×C4—612no—
394C22×C4—611no—
395C22×C4—1221no—
396C22×C4—1221no—
397C22×C4—1222no—
398C22×C4—1222no—
399C22×C4C4⋊#692311yescharacteristic
400C22×C4C22×#692311yescharacteristic
401M16—1224no—
402M16—1224no—
403M16—1224no—
404M16—1224no—
405M16—2442no—
406M16—2441no—
407M16—2441no—
408M16—2442no—
409M16—2442no—
410M16—2442no—
411M16—2442no—
412C2×C8—22no—
413C2×C8—21no—
414C2×C8—22no—
415C2×C8—611no—
416C2×C8—611no—
417C2×C8—1221no—
418C2×C8—1221no—
419C2×C8—1222no—
420C2×C8—1222no—
421C2×C8—1221no—
422C2×C8—1221no—
423C2×C8—1222no—
424C2×C8—1224no—
425C2×C8—1224no—
426C2×C8—1221no—
427C2×C8—1222no—
428C2×C8—2442no—
429C2×C8—2442no—
430C2×C8—2442no—
431C2×C8—2442no—
432C2×C8C22⋊#692311yescharacteristic
433C2×C8C22⋊#692311yescharacteristic
434C23—21no—
435C23—22no—
436C23—41no—
437C23—41no—
438C23—611no—
439C23—611no—
440C23—612no—
441C23—612no—
442C23—1222no—
443C23—1221no—
444C23—2441no—
445C23—2441no—
446C23—2441no—
447C23—2441no—
448C23C2×C4⋊#692311yescharacteristic
449Q8—2441no—
450Q8—2442no—
451Q8—2441no—
452D4—2441no—
453D4—2442no—
454D4—2441no—
455D4—2441no—
456D4—2442no—
457D4—2441no—
458D4—2441no—
459D4—2442no—
460D4—2441no—
461C2×C4—21no—
462C2×C4—22no—
463C2×C4—41no—
464C2×C4—42no—
465C2×C4—41no—
466C2×C4—611no—
467C2×C4—611no—
468C2×C4—612no—
469C2×C4—612no—
470C2×C4—611no—
471C2×C4—612no—
472C2×C4—611no—
473C2×C4—612no—
474C2×C4—612no—
475C2×C4—612no—
476C2×C4—612no—
477C2×C4—612no—
478C2×C4—611no—
479C2×C4—611no—
480C2×C4—1221no—
481C2×C4—1222no—
482C2×C4—2441no—
483C2×C4—2442no—
484C2×C4—2441no—
485C2×C4C2×C22⋊#692311yescharacteristic
486C2×C4#1451985611yescharacteristic
487C2×C4D4×#692312yes—
488C2×C4D4×#692312yes—
489C8—21no—
490C8—21no—
491C8—41no—
492C8—1221no—
493C8—1221no—
494C8—2444no—
495C8—2444no—
496C8—2441no—
497C22—21no—
498C22—21no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—82no—
503C22—611no—
504C22—612no—
505C22—611no—
506C22—1221no—
507C22—1221no—
508C22—1221no—
509C22—1221no—
510C22—4882no—
511C22—2442no—
512C22—2442no—
513C22—2441no—
514C22—2441no—
515C22—2441no—
516C22#1684070411yescharacteristic
517C22#1684070912yes—
518C4—41no—
519C4—611no—
520C4—612no—
521C4—611no—
522C4—2441no—
523C4#1684071011yescharacteristic
524C4#1684071212yes—
525C4#1684071411yescharacteristic
526C2—22no—
527C2—81no—
528C2—1221no—
529C2—1222no—
530C2—1221no—
531C2—4881no—
532C2#2146100211yescharacteristic
533C2#2146170311yescharacteristic
534C2#2146170411yescharacteristic
subgroupG/H
centerC2×C4#14519856
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C22⋊C8×C61C4
socleC22×C61#380
prime radicalC22×#11758222C22
cosocleC22×C4×D61C23
hypercenterC2×C22⋊C8#6923
hypocenterC61#11099
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C22⋊C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×D61⋊#108C2semidirect
3. #21461511C2semidirect
4. C2×#16840631C2semidirect
296. C61#11099semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×D61⋊#1082
C2×#168407482
#214615112
C2×#168406312
C2×#168397272
#1109961